BlockKrylovSchur/BlockKrylovSchurEpetraEx.cpp

Use Anasazi::BlockKrylovSchurSolMgr to solve a standard (not generalized) eigenvalue problem, using Epetra data structures.

// @HEADER
// *****************************************************************************
//                 Anasazi: Block Eigensolvers Package
//
// Copyright 2004 NTESS and the Anasazi contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
//  This example computes the specified eigenvalues of the discretized 2D Convection-Diffusion
//  equation using the block Krylov-Schur method.  This discretized operator is constructed as an
//  Epetra matrix, then passed into the Anasazi::EpetraOp to be used in the construction of the
//  Krylov decomposition.  The specifics of the block Krylov-Schur method can be set by the user.
#include "AnasaziBlockKrylovSchurSolMgr.hpp"
#include "AnasaziBasicEigenproblem.hpp"
#include "AnasaziConfigDefs.hpp"
#include "AnasaziEpetraAdapter.hpp"
#include "AnasaziBasicSort.hpp"
#include "Epetra_CrsMatrix.h"

#include "Teuchos_LAPACK.hpp"
#include "Teuchos_CommandLineProcessor.hpp"
#include "Teuchos_StandardCatchMacros.hpp"
#include "Teuchos_Assert.hpp"

#ifdef EPETRA_MPI
#include "Epetra_MpiComm.h"
#else
#include "Epetra_SerialComm.h"
#endif
#include "Epetra_Map.h"

int main(int argc, char *argv[]) {

  using std::cout;

#ifdef EPETRA_MPI
  // Initialize MPI
  MPI_Init(&argc,&argv);
#endif

  bool success = false;
  bool verbose = true;
  try {
#ifdef EPETRA_MPI
    Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
    Epetra_SerialComm Comm;
#endif
    bool boolret;
    int MyPID = Comm.MyPID();

    bool debug = false;
    bool dynXtraNev = false;
    std::string which("SM");
    int nx = 10;        // Discretization points in any one direction.
    int nev = 4;
    int blockSize = 1;
    int numBlocks = 20;

    Teuchos::CommandLineProcessor cmdp(false,true);
    cmdp.setOption("verbose","quiet",&verbose,"Print messages and results.");
    cmdp.setOption("debug","nodebug",&debug,"Print debugging information.");
    cmdp.setOption("sort",&which,"Targetted eigenvalues (SM,LM,SR,LR,SI,or LI).");
    cmdp.setOption("nx",&nx,"Number of discretization points in each direction; n=nx*nx.");
    cmdp.setOption("nev",&nev,"Number of eigenvalues to compute.");
    cmdp.setOption("blocksize",&blockSize,"Block Size.");
    cmdp.setOption("numblocks",&numBlocks,"Number of blocks for the Krylov-Schur form.");
    cmdp.setOption("dynrestart","nodynrestart",&dynXtraNev,"Use dynamic restart boundary to accelerate convergence.");
    if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
      MPI_Finalize();
#endif
      return -1;
    }

    typedef double ScalarType;
    typedef Teuchos::ScalarTraits<ScalarType>          SCT;
    typedef SCT::magnitudeType               MagnitudeType;
    typedef Epetra_MultiVector                          MV;
    typedef Epetra_Operator                             OP;
    typedef Anasazi::MultiVecTraits<ScalarType,MV>     MVT;
    typedef Anasazi::OperatorTraits<ScalarType,MV,OP>  OPT;

    //  Dimension of the matrix
    int NumGlobalElements = nx*nx;  // Size of matrix nx*nx

    // Construct a Map that puts approximately the same number of
    // equations on each processor.

    Epetra_Map Map(NumGlobalElements, 0, Comm);

    // Get update list and number of local equations from newly created Map.

    int NumMyElements = Map.NumMyElements();

    std::vector<int> MyGlobalElements(NumMyElements);
    Map.MyGlobalElements(&MyGlobalElements[0]);

    // Create an integer vector NumNz that is used to build the Petra Matrix.
    // NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation
    // on this processor
    std::vector<int> NumNz(NumMyElements);

    /* We are building a matrix of block structure:

       | T -I          |
       |-I  T -I       |
       |   -I  T       |
       |        ...  -I|
       |           -I T|

       where each block is dimension nx by nx and the matrix is on the order of
       nx*nx.  The block T is a tridiagonal matrix.
       */

    for (int i=0; i<NumMyElements; i++) {
      if (MyGlobalElements[i] == 0 || MyGlobalElements[i] == NumGlobalElements-1 ||
          MyGlobalElements[i] == nx-1 || MyGlobalElements[i] == nx*(nx-1) ) {
        NumNz[i] = 3;
      }
      else if (MyGlobalElements[i] < nx || MyGlobalElements[i] > nx*(nx-1) ||
          MyGlobalElements[i]%nx == 0 || (MyGlobalElements[i]+1)%nx == 0) {
        NumNz[i] = 4;
      }
      else {
        NumNz[i] = 5;
      }
    }

    // Create an Epetra_Matrix

    Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Epetra_DataAccess::Copy, Map, &NumNz[0]) );

    // Diffusion coefficient, can be set by user.
    // When rho*h/2 <= 1, the discrete convection-diffusion operator has real eigenvalues.
    // When rho*h/2 > 1, the operator has complex eigenvalues.
    //double rho = 2*nx+1;
    double rho = 0.0;

    // Compute coefficients for discrete convection-diffution operator
    const double one = 1.0;
    std::vector<double> Values(4);
    std::vector<int> Indices(4);
    double h = one /(nx+1);
    double h2 = h*h;
    double c = 5.0e-01*rho/ h;
    Values[0] = -one/h2 - c; Values[1] = -one/h2 + c; Values[2] = -one/h2; Values[3]= -one/h2;
    double diag = 4.0 / h2;
    int NumEntries, info;

    for (int i=0; i<NumMyElements; i++)
    {
      if (MyGlobalElements[i]==0)
      {
        Indices[0] = 1;
        Indices[1] = nx;
        NumEntries = 2;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if (MyGlobalElements[i] == nx*(nx-1))
      {
        Indices[0] = nx*(nx-1)+1;
        Indices[1] = nx*(nx-2);
        NumEntries = 2;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if (MyGlobalElements[i] == nx-1)
      {
        Indices[0] = nx-2;
        NumEntries = 1;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
        Indices[0] = 2*nx-1;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if (MyGlobalElements[i] == NumGlobalElements-1)
      {
        Indices[0] = NumGlobalElements-2;
        NumEntries = 1;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
        Indices[0] = nx*(nx-1)-1;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if (MyGlobalElements[i] < nx)
      {
        Indices[0] = MyGlobalElements[i]-1;
        Indices[1] = MyGlobalElements[i]+1;
        Indices[2] = MyGlobalElements[i]+nx;
        NumEntries = 3;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if (MyGlobalElements[i] > nx*(nx-1))
      {
        Indices[0] = MyGlobalElements[i]-1;
        Indices[1] = MyGlobalElements[i]+1;
        Indices[2] = MyGlobalElements[i]-nx;
        NumEntries = 3;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if (MyGlobalElements[i]%nx == 0)
      {
        Indices[0] = MyGlobalElements[i]+1;
        Indices[1] = MyGlobalElements[i]-nx;
        Indices[2] = MyGlobalElements[i]+nx;
        NumEntries = 3;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else if ((MyGlobalElements[i]+1)%nx == 0)
      {
        Indices[0] = MyGlobalElements[i]-nx;
        Indices[1] = MyGlobalElements[i]+nx;
        NumEntries = 2;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
        Indices[0] = MyGlobalElements[i]-1;
        NumEntries = 1;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      else
      {
        Indices[0] = MyGlobalElements[i]-1;
        Indices[1] = MyGlobalElements[i]+1;
        Indices[2] = MyGlobalElements[i]-nx;
        Indices[3] = MyGlobalElements[i]+nx;
        NumEntries = 4;
        info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
        TEUCHOS_ASSERT( info==0 );
      }
      // Put in the diagonal entry
      info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);
      TEUCHOS_ASSERT( info==0 );
    }

    // Finish up
    info = A->FillComplete();
    TEUCHOS_ASSERT( info==0 );
    A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks

    //************************************
    // Start the block Arnoldi iteration
    //***********************************
    //
    //  Variables used for the Block Krylov Schur Method
    //
    int maxRestarts = 500;
    //int stepSize = 5;
    double tol = 1e-8;

    // Create a sort manager to pass into the block Krylov-Schur solver manager
    // -->  Make sure the reference-counted pointer is of type Anasazi::SortManager<>
    // -->  The block Krylov-Schur solver manager uses Anasazi::BasicSort<> by default,
    //      so you can also pass in the parameter "Which", instead of a sort manager.
    Teuchos::RCP<Anasazi::SortManager<MagnitudeType> > MySort =
      Teuchos::rcp( new Anasazi::BasicSort<MagnitudeType>( which ) );

    // Set verbosity level
    int verbosity = Anasazi::Errors + Anasazi::Warnings;
    if (verbose) {
      verbosity += Anasazi::FinalSummary + Anasazi::TimingDetails;
    }
    if (debug) {
      verbosity += Anasazi::Debug;
    }
    //
    // Create parameter list to pass into solver manager
    //
    Teuchos::ParameterList MyPL;
    MyPL.set( "Verbosity", verbosity );
    MyPL.set( "Sort Manager", MySort );
    //MyPL.set( "Which", which );
    MyPL.set( "Block Size", blockSize );
    MyPL.set( "Num Blocks", numBlocks );
    MyPL.set( "Maximum Restarts", maxRestarts );
    //MyPL.set( "Step Size", stepSize );
    MyPL.set( "Convergence Tolerance", tol );
    MyPL.set("Dynamic Extra NEV",dynXtraNev);

    // Create an Epetra_MultiVector for an initial vector to start the solver.
    // Note:  This needs to have the same number of columns as the blocksize.
    Teuchos::RCP<Epetra_MultiVector> ivec = Teuchos::rcp( new Epetra_MultiVector(Map, blockSize) );
    ivec->Random();

    // Create the eigenproblem.
    Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem =
      Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(A, ivec) );

    // Inform the eigenproblem that the operator A is symmetric
    MyProblem->setHermitian(rho==0.0);

    // Set the number of eigenvalues requested
    MyProblem->setNEV( nev );

    // Inform the eigenproblem that you are finishing passing it information
    boolret = MyProblem->setProblem();
    if (boolret != true) {
      if (verbose && MyPID == 0) {
        std::cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << std::endl;
      }
#ifdef HAVE_MPI
      MPI_Finalize() ;
#endif
      return -1;
    }

    // Initialize the Block Arnoldi solver
    Anasazi::BlockKrylovSchurSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);

    // Solve the problem to the specified tolerances or length
    Anasazi::ReturnType returnCode = MySolverMgr.solve();
    if (returnCode != Anasazi::Converged && MyPID==0 && verbose) {
      std::cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << std::endl;
    }

    // Get the Ritz values from the eigensolver
    std::vector<Anasazi::Value<double> > ritzValues = MySolverMgr.getRitzValues();

    // Output computed eigenvalues and their direct residuals
    if (verbose && MyPID==0) {
      int numritz = (int)ritzValues.size();
      std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
      std::cout<<std::endl<< "Computed Ritz Values"<< std::endl;
      if (MyProblem->isHermitian()) {
        std::cout<< std::setw(16) << "Real Part"
          << std::endl;
        std::cout<<"-----------------------------------------------------------"<<std::endl;
        for (int i=0; i<numritz; i++) {
          std::cout<< std::setw(16) << ritzValues[i].realpart
            << std::endl;
        }
        std::cout<<"-----------------------------------------------------------"<<std::endl;
      }
      else {
        std::cout<< std::setw(16) << "Real Part"
          << std::setw(16) << "Imag Part"
          << std::endl;
        std::cout<<"-----------------------------------------------------------"<<std::endl;
        for (int i=0; i<numritz; i++) {
          std::cout<< std::setw(16) << ritzValues[i].realpart
            << std::setw(16) << ritzValues[i].imagpart
            << std::endl;
        }
        std::cout<<"-----------------------------------------------------------"<<std::endl;
      }
    }

    // Get the eigenvalues and eigenvectors from the eigenproblem
    Anasazi::Eigensolution<ScalarType,MV> sol = MyProblem->getSolution();
    std::vector<Anasazi::Value<ScalarType> > evals = sol.Evals;
    Teuchos::RCP<MV> evecs = sol.Evecs;
    std::vector<int> index = sol.index;
    int numev = sol.numVecs;

    if (numev > 0) {
      // Compute residuals.
      Teuchos::LAPACK<int,double> lapack;
      std::vector<double> normA(numev);

      if (MyProblem->isHermitian()) {
        // Get storage
        Epetra_MultiVector Aevecs(Map,numev);
        Teuchos::SerialDenseMatrix<int,double> B(numev,numev);
        B.putScalar(0.0);
        for (int i=0; i<numev; i++) {B(i,i) = evals[i].realpart;}

        // Compute A*evecs
        OPT::Apply( *A, *evecs, Aevecs );

        // Compute A*evecs - lambda*evecs and its norm
        MVT::MvTimesMatAddMv( -1.0, *evecs, B, 1.0, Aevecs );
        MVT::MvNorm( Aevecs, normA );

        // Scale the norms by the eigenvalue
        for (int i=0; i<numev; i++) {
          normA[i] /= Teuchos::ScalarTraits<double>::magnitude( evals[i].realpart );
        }
      } else {
        // The problem is non-Hermitian.
        int i=0;
        std::vector<int> curind(1);
        std::vector<double> resnorm(1), tempnrm(1);
        Teuchos::RCP<MV> tempAevec;
        Teuchos::RCP<const MV> evecr, eveci;
        Epetra_MultiVector Aevec(Map,numev);

        // Compute A*evecs
        OPT::Apply( *A, *evecs, Aevec );

        Teuchos::SerialDenseMatrix<int,double> Breal(1,1), Bimag(1,1);
        while (i<numev) {
          if (index[i]==0) {
            // Get a view of the current eigenvector (evecr)
            curind[0] = i;
            evecr = MVT::CloneView( *evecs, curind );

            // Get a copy of A*evecr
            tempAevec = MVT::CloneCopy( Aevec, curind );

            // Compute A*evecr - lambda*evecr
            Breal(0,0) = evals[i].realpart;
            MVT::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );

            // Compute the norm of the residual and increment counter
            MVT::MvNorm( *tempAevec, resnorm );
            normA[i] = resnorm[0]/Teuchos::ScalarTraits<MagnitudeType>::magnitude( evals[i].realpart );
            i++;
          } else {
            // Get a view of the real part of the eigenvector (evecr)
            curind[0] = i;
            evecr = MVT::CloneView( *evecs, curind );

            // Get a copy of A*evecr
            tempAevec = MVT::CloneCopy( Aevec, curind );

            // Get a view of the imaginary part of the eigenvector (eveci)
            curind[0] = i+1;
            eveci = MVT::CloneView( *evecs, curind );

            // Set the eigenvalue into Breal and Bimag
            Breal(0,0) = evals[i].realpart;
            Bimag(0,0) = evals[i].imagpart;

            // Compute A*evecr - evecr*lambdar + eveci*lambdai
            MVT::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
            MVT::MvTimesMatAddMv( 1.0, *eveci, Bimag, 1.0, *tempAevec );
            MVT::MvNorm( *tempAevec, tempnrm );

            // Get a copy of A*eveci
            tempAevec = MVT::CloneCopy( Aevec, curind );

            // Compute A*eveci - eveci*lambdar - evecr*lambdai
            MVT::MvTimesMatAddMv( -1.0, *evecr, Bimag, 1.0, *tempAevec );
            MVT::MvTimesMatAddMv( -1.0, *eveci, Breal, 1.0, *tempAevec );
            MVT::MvNorm( *tempAevec, resnorm );

            // Compute the norms and scale by magnitude of eigenvalue
            normA[i] = lapack.LAPY2( tempnrm[0], resnorm[0] ) /
              lapack.LAPY2( evals[i].realpart, evals[i].imagpart );
            normA[i+1] = normA[i];

            i=i+2;
          }
        }
      }

      // Output computed eigenvalues and their direct residuals
      if (verbose && MyPID==0) {
        std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
        std::cout<<std::endl<< "Actual Residuals"<<std::endl;
        if (MyProblem->isHermitian()) {
          std::cout<< std::setw(16) << "Real Part"
            << std::setw(20) << "Direct Residual"<< std::endl;
          std::cout<<"-----------------------------------------------------------"<<std::endl;
          for (int i=0; i<numev; i++) {
            std::cout<< std::setw(16) << evals[i].realpart
              << std::setw(20) << normA[i] << std::endl;
          }
          std::cout<<"-----------------------------------------------------------"<<std::endl;
        }
        else {
          std::cout<< std::setw(16) << "Real Part"
            << std::setw(16) << "Imag Part"
            << std::setw(20) << "Direct Residual"<< std::endl;
          std::cout<<"-----------------------------------------------------------"<<std::endl;
          for (int i=0; i<numev; i++) {
            std::cout<< std::setw(16) << evals[i].realpart
              << std::setw(16) << evals[i].imagpart
              << std::setw(20) << normA[i] << std::endl;
          }
          std::cout<<"-----------------------------------------------------------"<<std::endl;
        }
      }
    }

    success = true;
  }
  TEUCHOS_STANDARD_CATCH_STATEMENTS(verbose, std::cerr, success);

#ifdef EPETRA_MPI
  MPI_Finalize();
#endif

  return ( success ? EXIT_SUCCESS : EXIT_FAILURE );
}